2­1 Rational numbers Converting Frac and Dec.notebook
October 04, 2016
2-1
Rational Numbers
and Converting back and forth between
Fractions and Decimals
Sep 22­4:12 PM
Objective: To understand the sets of numbers and how they are related. To be able to convert fractions and mixed numbers into decimals. To be able to convert terminating decimals and simple repeating decimals into fractions.
Skill/Virtue: For other decimals, you will be using equations to find the fractions, but for now we will use the shortcut found from this way of doing things. Knowing the qualities of the sets that numbers are in is useful for higher mathematics and says a lot about the number.
Sep 22­4:12 PM
1
2­1 Rational numbers Converting Frac and Dec.notebook
LESSON 5‐2
RATIONAL NUMBERS
October 04, 2016
Imaginary Numbers
Natural Numbers
1,2,3,4...
Whole Numbers 0, 1, 2, 3..... ­negative sign INSIDE the
square root
­zero as the denominator
Integers
positive and negative numbers all found on the integer line ...­3, ­2, ­1, 0, 1, 2, 3...
Rational Numbers
fractions and decimals that terminate or repeat 4.5, ­1.267, 3/4, ­1/8, 5.432432432...
Irrational Numbers
­Decimals that do not terminate and do not repeat
­square roots of non perfect squares
Mar 23­3:39 PM
Natural Numbers­ all positive integers, the counting numbers
Irrational numbers­ numbers with decimals that do not repeat and do not terminate.
3.1359275... 67
Mar 27­1:40 PM
2
2­1 Rational numbers Converting Frac and Dec.notebook
October 04, 2016
Name all the sets of numbers to which each number belongs. 1. 8
rational, integer, natural, whole number
rational
2. 1/2
PULL
PULL
3. 2/5
rational
4. 12
rational, integer, natural, whole number
PULL
5. ­ √64
rational, integer
6.
rational
0.2
PULL
PULL
irrational
7.
PULL
PULL
0.1313313...
Mar 27­1:46 PM
Convert Fractions to Decimals
Divide the fraction part using long division, the decimal you get tags along behind the whole number part.
3
5
­4
3
8
Sep 22­4:05 PM
3
2­1 Rational numbers Converting Frac and Dec.notebook
The numerator is the number(s) after the decimal The denominator is the place value of the last digit. THEN SIMPLIFY.
Place Value
un
On
es
Te
nth
Hu s
nd
Th redt
hs
ou
s
Te
a
n­t nd
ho ths
H
u
s
dre andt
hs
d­t
Mi
h
ou
llio
sa
nth
nd
s
th
s
Convert Decimals To Fractions
October 04, 2016
0.237512
29689 125000
Sep 27­7:06 AM
NUMERATOR
0.45 45
100
Hundredths place
Dec 2­9:33 AM
4
2­1 Rational numbers Converting Frac and Dec.notebook
October 04, 2016
NUMERATOR
9.045 45 9
1000
Thousandths place
Dec 2­9:33 AM
Write each decimal as a fraction in simplest form.
1.) 0.5
4.) 0.0056
2.) 2.36
5.) 5.375
3.) 0.85
Sep 27­7:13 AM
5
2­1 Rational numbers Converting Frac and Dec.notebook
Converting a repeating decimal to fraction form.
October 04, 2016
1­ Put the numbers that are repeating as the numerator. 2­ Count the number of digits that repeat.
3­ If only one digit repeated put 9 as the denominator. If two digits repeated put 99 as the denominator. THEN SIMPLIFY.
0.3 = 0.3333...
0.2 = 0.222.....
3 = 1
9 3
2 9
5.42 = 5.424242...
14
42 = 99 33
5
5
5.423 Dec 8­12:02 PM
Apr 2­1:39 PM
6
2­1 Rational numbers Converting Frac and Dec.notebook
October 04, 2016
Summary
Objective: To understand the sets of numbers and how they are related. To be able to convert fractions and mixed numbers into decimals. To be able to convert terminating decimals and simple repeating decimals into fractions.
Skill/Virtue: For other decimals, you will be using equations to find the fractions, but for now we will use the shortcut found from this way of doing things. Knowing the qualities of the sets that numbers are in is useful for higher mathematics and says a lot about the number.
Assignment: Workbook pg. 11
Nov 15­3:55 PM
7